Average Error: 0.2 → 0.0
Time: 6.4s
Precision: 64
Internal Precision: 128
\[\left(d1 \cdot 10 + d1 \cdot d2\right) + d1 \cdot 20\]
↓
\[d1 \cdot 30 + d2 \cdot d1\]

Error

Bits error versus d1

Bits error versus d2

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.2
Target0.0
Herbie0.0
\[d1 \cdot \left(30 + d2\right)\]

Derivation

  1. Initial program 0.2

    \[\left(d1 \cdot 10 + d1 \cdot d2\right) + d1 \cdot 20\]

  2. Simplified0.0

    \[\leadsto \color{blue}{d1 \cdot \left(30 + d2\right)}\]
  3. Using strategy rm

  4. Applied distribute-lft-in0.0

    \[\leadsto \color{blue}{d1 \cdot 30 + d1 \cdot d2}\]

  5. Final simplification0.0

    \[\leadsto d1 \cdot 30 + d2 \cdot d1\]

Reproduce

herbie shell --seed 2019004 
(FPCore (d1 d2)
  :name "FastMath test2"

  :herbie-target
  (* d1 (+ 30 d2))

  (+ (+ (* d1 10) (* d1 d2)) (* d1 20)))

Details

Time bar (total: 5.9s)Debug log

sample53.0ms

Algorithm
intervals

simplify51.0ms

Counts
1 → 1
Calls

1 calls. Slowest were:

51.0ms
(+ (+ (* d1 10) (* d1 d2)) (* d1 20))

prune18.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize6.0ms

Local error

Found 1 expressions with local error:

0.0b
(* d1 (+ 30 d2))

rewrite2.0ms

Algorithm
rewrite-expression-head
Counts
1 → 15
Calls

1 calls. Slowest were:

2.0ms
(* d1 (+ 30 d2))

series22.0ms

Counts
1 → 3
Calls

1 calls. Slowest were:

22.0ms
(* d1 (+ 30 d2))

simplify98.0ms

Counts
10 → 18
Calls

10 calls. Slowest were:

64.0ms
(+ (* 30 30) (- (* d2 d2) (* 30 d2)))
9.0ms
(+ (* d2 d1) (* 30 d1))
8.0ms
(+ (* d2 d1) (* 30 d1))

prune114.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize7.0ms

Local error

Found 1 expressions with local error:

0.0b
(+ (* d1 30) (* d1 d2))

rewrite2.0ms

Algorithm
rewrite-expression-head
Counts
1 → 12
Calls

1 calls. Slowest were:

2.0ms
(+ (* d1 30) (* d1 d2))

series24.0ms

Counts
1 → 3
Calls

1 calls. Slowest were:

24.0ms
(+ (* d1 30) (* d1 d2))

simplify49.0ms

Counts
5 → 15
Calls

5 calls. Slowest were:

18.0ms
(* (exp (* d1 30)) (exp (* d1 d2)))
9.0ms
(+ (* d2 d1) (* 30 d1))
9.0ms
(+ (* d2 d1) (* 30 d1))

prune138.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize21.0ms

Local error

Found 2 expressions with local error:

0.1b
(+ (+ (* d1 10) (* d1 d2)) (* d1 20))
0.0b
(+ (* d1 10) (* d1 d2))

rewrite23.0ms

Algorithm
rewrite-expression-head
Counts
2 → 26
Calls

2 calls. Slowest were:

19.0ms
(+ (+ (* d1 10) (* d1 d2)) (* d1 20))
4.0ms
(+ (* d1 10) (* d1 d2))

series60.0ms

Counts
2 → 6
Calls

2 calls. Slowest were:

31.0ms
(+ (+ (* d1 10) (* d1 d2)) (* d1 20))
29.0ms
(+ (* d1 10) (* d1 d2))

simplify205.0ms

Counts
12 → 32
Calls

12 calls. Slowest were:

84.0ms
(* (exp (+ (* d1 10) (* d1 d2))) (exp (* d1 20)))
65.0ms
(* (* (exp (* d1 10)) (exp (* d1 d2))) (exp (* d1 20)))
16.0ms
(* (exp (* d1 10)) (exp (* d1 d2)))

prune217.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* d1 (sqrt (+ 30 d2))) (sqrt (+ 30 d2)))
0.1b
(* d1 (sqrt (+ 30 d2)))
0.0b
(sqrt (+ 30 d2))
0.0b
(sqrt (+ 30 d2))

rewrite21.0ms

Algorithm
rewrite-expression-head
Counts
4 → 70
Calls

4 calls. Slowest were:

14.0ms
(* (* d1 (sqrt (+ 30 d2))) (sqrt (+ 30 d2)))
4.0ms
(* d1 (sqrt (+ 30 d2)))
1.0ms
(sqrt (+ 30 d2))

series100.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

28.0ms
(* (* d1 (sqrt (+ 30 d2))) (sqrt (+ 30 d2)))
27.0ms
(* d1 (sqrt (+ 30 d2)))
25.0ms
(sqrt (+ 30 d2))
20.0ms
(sqrt (+ 30 d2))

simplify2.9s

Counts
53 → 82
Calls

53 calls. Slowest were:

637.0ms
(* (* (* (* d1 (sqrt (+ 30 d2))) (* d1 (sqrt (+ 30 d2)))) (* d1 (sqrt (+ 30 d2)))) (* (* (sqrt (+ 30 d2)) (sqrt (+ 30 d2))) (sqrt (+ 30 d2))))
420.0ms
(* (sqrt (+ (* 30 30) (- (* d2 d2) (* 30 d2)))) (sqrt (- 30 d2)))
296.0ms
(- (+ (* 1/2 (/ d2 (sqrt 30))) (sqrt 30)) (* 1/8 (/ (pow d2 2) (pow (sqrt 30) 3))))

prune652.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes112.0ms

Accuracy

0% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 0.0b

bsearch1.0ms

end0.0ms

sample1.0s

Algorithm
intervals